To join the discussion on how to define Critical Thinking in Math, click link above ^
According to EvCC Math Faculty Critical Thinking is...
Analysis - the ability to recognize and sort problems Synthesis - the ability to organize a multiplicity of skills and tools to solve problems
and... Inference - the ability to use given data to guide decision making.
or Identification and evaluation of evidence, or data, to guide decision making.
or Assessment - reflecting on the conclusion as well as the ability to explain your conclusions
Analysis in math is about breaking a problem down into parts, i.e. recognizing information, assumptions, relevant concepts (skills or tools). Evaluation is about using logic to judge accuracy, clarity, precision and significance of results.
Identification and evaluation of evidence, or data, to guide decision making.
Qualitative translation: Identifying the important numerical relationships in a given situation and translating these into useful expressions/equations Symbolic reasoning: Applying laws and properties of mathematical structures to deduce the values of other quantities in the given situation. Evaluation (Decision making): Translation and analysis of the deductions made.
Problem solving process is an instant of critical thinking. In this way, analysis correspond to planning/understanding, while synthesis correspond to solving. Therefore, evaluation, or look back can also be very interesting to consider. Evaluation is not merely look back at the end. It can be used during the analysis and/or synthesis: to compare different approaches so that a suitable choice can be made (think about different approaches for solving a system of two linear equations in two variables, or solving a quadratic equation), and to evaluate (intermediate) results.
Still, I think evaluation is somehow already (or can easily be) incorporated in analysis and synthesis: those two are essential, yet broad enough to highlight critical thinking (thus all the stages of problem solving). Thus, I vote for the essential, yet broad enough and manageable definition of critical thinking proposed in your mail: analysis and synthesis.
The ability to think deeper, understand the different components of the problem, and try to come up with a strategic plan to solve it, possibly using multiple skills and tools to analyze the problem.
Looking at the big picture and reducing the problem down to the bare bones (picking out the key ideas to work with and eliminating the extraneous material).
To join the discussion on how to define Critical Thinking in Math, click link above ^
According to EvCC Math Faculty Critical Thinking is...
Analysis - the ability to recognize and sort problems
Synthesis - the ability to organize a multiplicity of skills and tools to solve problems
and...
Inference - the ability to use given data to guide decision making.
or
Identification and evaluation of evidence, or data, to guide decision making.
or
Assessment - reflecting on the conclusion as well as the ability to explain your conclusions
Analysis in math is about breaking a problem down into parts, i.e. recognizing information, assumptions, relevant concepts (skills or tools).
Evaluation is about using logic to judge accuracy, clarity, precision and significance of results.
Identification and evaluation of evidence, or data, to guide decision making.
Qualitative translation: Identifying the important numerical relationships in a given situation and translating these into useful expressions/equations
Symbolic reasoning: Applying laws and properties of mathematical structures to deduce the values of other quantities in the given situation.
Evaluation (Decision making): Translation and analysis of the deductions made.
Problem solving process is an instant of critical thinking. In this way, analysis correspond to planning/understanding, while synthesis correspond to solving. Therefore, evaluation, or look back can also be very interesting to consider. Evaluation is not merely look back at the end. It can be used during the analysis and/or synthesis: to compare different approaches so that a suitable choice can be made (think about different approaches for solving a system of two linear equations in two variables, or solving a quadratic equation), and to evaluate (intermediate) results.
Still, I think evaluation is somehow already (or can easily be) incorporated in analysis and synthesis: those two are essential, yet broad enough to highlight critical thinking (thus all the stages of problem solving). Thus, I vote for the essential, yet broad enough and manageable definition of critical thinking proposed in your mail: analysis and synthesis.
The ability to think deeper, understand the different components of the problem, and try to come up with a strategic plan to solve it, possibly using multiple skills and tools to analyze the problem.
Looking at the big picture and reducing the problem down to the bare bones (picking out the key ideas to work with and eliminating the extraneous material).
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